Live Exercise 2: Replacement Effect and Social Value of Innovation

MSc-level Industrial Organisation course at the University of St Andrews

Group exercise (≈20 minutes)

• Work in groups of 2–3.
• Show all intermediate steps — the algebra matters.
• Full market coverage assumed throughout.

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Problem: Replacement effect and social value

A pharmaceutical company has discovered a new manufacturing process (Tech P) that reduces the marginal cost of producing a drug from \(c_0 = 60\) to \(c_1 = 30\). Market demand for the drug is

\[ P(Q) = 100 - Q. \]

Assume Tech P is available exclusively to the one firm that acquires it (patent protection is perfect).

(a) Is the innovation drastic?

Use the monopoly pricing formula to determine whether Tech P is drastic or non-drastic. State the condition and evaluate it numerically.

Recall: a process innovation is drastic if \(P^m(c_1) < c_0\), where \(P^m(c) = \tfrac{A+c}{2}\) under linear demand \(P = A - Q\).

(b) Monopoly and competitive WTP

Compute the maximum willingness to pay (WTP) for Tech P of:

1. a monopolist (not threatened by entry)
2. a competitive innovator — a firm that operates in a competitive market before acquiring the patent, then gains exclusive rights to Tech P

Hint for (2): use your result from (a) to determine whether the competitive innovator limit-prices at \(p = c_0\) after acquiring the patent.

(c) Social planner’s value

For linear demand \(P = A - Q\) with efficient production (price equals marginal cost), total surplus is \(W(c) = \tfrac{(A-c)^2}{2}\).

1. Compute the social planner’s value of the innovation, \(\Delta W = W(c_1) - W(c_0)\).
2. Arrange the three values — \(\Delta\pi^m\), competitive WTP, \(\Delta W\) — in increasing order.
3. State Arrow’s replacement effect in one sentence. Using the numbers from (b), explain what drives the gap between \(\Delta\pi^m\) and the competitive WTP. Why is \(\Delta W\) larger than both?

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